How to sync music to 1st generation 1GB iPod?

I recently found my old iPod and wanted to use it for music instead of using up storage on my phone. However, when I plug it into my computer and open iTunes it doesn't show/recognize my iPod as being connected. The green light stays on the iPod while the iPod is plugged in, but like I said before it doesn't show up on iTunes. Is this just an issue with the iPod itself?